Using well known facts about group and representation theory, we show that field computations can be considerably reduced. In the case where the geometry exhibits some sort of symmetry, one can achieve faster processing and needs less memory by a factor of two or even more. The technique described below may find broad application in all field computation methods, which take advantage of linear vector space properties. To illustrate our technique we apply it to the image method, the point-matching method, the finite differences, the finite-elements-method and to the method of moments. We begin with a simple 2D-problem taken from electrostatics. Its boundary has only one symmetry axis. In this case the application of group theory leads to the well known symmetrical and antisymmetrical parts. For more complex symmetries we show that intuitive symmetry considerations may be misleading and give results received by the representation theory.